A linear algorithm for constructing the polygon adjacency relation in iso-surfaces of 3D images

  • Serge Miguet
  • Jean-Marc Nicod
  • David Sarrut
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1347)


This paper proposes an optimal algorithm for constructing the surface adjacency relation in a list of polygons extracted from 3D medical images. The discrete nature of data allows us to build this adjacency relation in a time proportional to the number of triangles T. We have payed a special attention on the memory requirements, since our method takes as input the surface extracted by the Marching-Cubes algorithm and does not make reference to the initial 3D dataset. Moreover, no additional temporary storage is needed to compute the relation.


Additional Memory Distinct Triangle Naive Algorithm Computer Imagery Efficient Parallel Implementation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. [CLR90]
    Thomas Cormen, Charles Leiserson, and Ronald Rivest. Introduction to Algorithms. MIT Press, 1990.Google Scholar
  2. [Lac96]
    Jacques-Olivier Lachaud. Topologically defined isosurfaces. In Serge Miguet, Annie Montanvert, and Stéphane Ubéda, editors, Discrete Geometry for Computer Imagery, volume 1176 of Lecture Notes in Computer Science, pages 245–256. Springer, November 1996.Google Scholar
  3. [LB94]
    Jacques-Olivier Lachaud and Eric Bainville. A discrete model following topological modifications of volumes. In Jean-Marc Chassery and Annick Montanvert, editors, Discrete geometry for computer imagery, pages 183–194, Grenoble (France), September 1994.Google Scholar
  4. [LC87]
    William E. Lorensen and Harvey E. Cline. Marching cubes: a high resolution 3D surface construction algorithm. Computer Graphics, 21(4):163–169, July 1987.Google Scholar
  5. [Mig95]
    Serge Miguet. Un environnement parallèle pour l'imagerie 3D. Mémoire d'habilitation à diriger des recherches, Laboratoire de l'informatique du Parallélisme, 46 allée d'Italie, 69364 Lyon Cedex 07, December 1995.Google Scholar
  6. [MN95]
    Serge Miguet and Jean-Marc Nicod. An optimal parallel iso-surface extraction algorithm. In Fourth International Workshop on Parallel Image Analysis (IWPIA'95,), pages 65–78. Laboratoire de l'Informatique du Parallélisme, ENS Lyon (France), December 1995.Google Scholar
  7. [Per94]
    Lament Perroton. Segmentation Parallèle d'Images Volumiques. PhD thesis, Ecole Normale Supérieure de Lyon, December 1994.Google Scholar
  8. [ZN94]
    Meiyun Zheng and H.T. Nguyen. An Efficient Parallel Implementation of the Marching-cubes Algorithm. In L. Decker, W. Smit, and J.C. Zuidervaaxt, editors, Massively Parallel Processing Applications and Development, pages 903–910, 1994.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Serge Miguet
    • 1
  • Jean-Marc Nicod
    • 2
  • David Sarrut
    • 3
  1. 1.Laboratoire ERIC Bât. LUniv. Lyon IIBronFrance
  2. 2.LIBIUT Belfort-MontbeliardBelfort Cedex
  3. 3.Laboratoire ERIC Bât. LUniv. Lyon IIBronFrance

Personalised recommendations